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Chapter 2. Descriptive Statistics

Means and Averages

In the previous chapter, I mentioned three summary
statistics—mean, variance, and median—without explaining what they are.
So before we go any farther, let’s take care of that.

If you have a sample of n values,
xi, the
mean, μ, is the sum of the values divided by the
number of values; in other words

The words “mean” and “average” are sometimes used interchangeably,
but I will maintain this distinction:

The “mean” of a sample is the summary statistic computed with
the previous formula.

An “average” is one of many summary statistics you might
choose to describe the typical value or the central tendency of a sample.

Sometimes the mean is a good description of a set of values. For
example, apples are all pretty much the same size (at least the ones
sold in supermarkets). So if I buy six apples and the total weight is
three pounds, it would be reasonable to conclude that they are about a
half pound each.

But pumpkins are more diverse. Suppose I grow several varieties in
my garden, and one day I harvest three decorative pumpkins that are one
pound each, two pie pumpkins that are three pounds each, and one
Atlantic Giant pumpkin that weighs 591 pounds. The mean of this
sample is 100 pounds, but if I told you “The average pumpkin in my
garden is 100 pounds,” that would be wrong, or at least
misleading.

In this example, there is no meaningful average ...

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